Problem: What is the value of the following logarithm? $\log_{5} 5$
Answer: If $b^y = x$ , then $\log_{b} x = y$ Therefore, we want to find the value $y$ such that $5^{y} = 5$ Any number raised to the power $1$ is simply itself, so $5^{1} = 5$ and thus $\log_{5} 5 = 1$.